Identify the amplitude and period of the following functions.
$p\(\left\)(t\(\right\))=2.5\(\sin\]\left\)(\(\frac\)12\(\left\)(t-3\(\right\))\(\right\))$

{Use of Tech} Polynomial calculations

Find a polynomial ƒ that satisfies the following properties. (Hint: Determine the degree of ƒ; then substitute a polynomial of that degree and solve for its coefficients.)

ƒ(ƒ(x)) = x⁴ - 12x² + 30

Area of a circular sector Prove that the area of a sector of a circle of radius r associated with a central angle $\(\theta\)$ (measured in radians) is $A=\(\frac\)12r^2\(\theta\)$.

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{Use of Tech} Triple intersection Graph the functions f(x) = x³,g(x)=3^x, and h(x)=x^x and find their common intersection point (exactly).

Identify the amplitude and period of the following functions.

$f\(\left\)(\(\pi\]\right\))=2\(\sin\)2\(\theta\)$

Identify the amplitude and period of the following functions.

$q\(\left\)(x\(\right\))=3.6\(\cos\[\left\)(\(\frac{\pi x}{24}\]\right\))$

Identify the amplitude and period of the following functions.

$g\(\left\)(\(\theta\]\right\))=3\(\cos\[\left\)(\(\frac{\theta}{3}\]\right\))$